Subjects algebra

Book Pen Price

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1. **State the problem:** We are given that the price of a book is 4 more than the price of a pen. The total cost of 2 books and 3 pens is 38. We need to find the cost of one pen and one book. 2. **Define variables:** Let the price of one pen be $p$. Then the price of one book is $p + 4$. 3. **Write the equation for total cost:** The total cost of 2 books and 3 pens is: $$2(p + 4) + 3p = 38$$ 4. **Simplify the equation:** $$2p + 8 + 3p = 38$$ $$5p + 8 = 38$$ 5. **Solve for $p$:** $$5p = 38 - 8$$ $$5p = 30$$ $$p = \frac{30}{5} = 6$$ 6. **Find the price of one book:** $$p + 4 = 6 + 4 = 10$$ **Final answer:** The price of one pen is 6 and the price of one book is 10.